I've mentioned this before but the choice of oils is usually decided by the engine builder and may or may not be influenced by oil sponsors/providers.
If a top NASCAR team is sponsored by an oil company (primary or other sponsor) you can bet they'll use their sponsors oil. Why not, they get it for free!!
Do the oil mfr's create a special batch of oils for their NASCAR teams? My guess is "probably". This is a pretty tightly held secret between the engine shop and the oil mfr. If the engine builder feels the off-the-shelf product is good enough, I'm sure he'll use it. If not, I'm sure the oil mfr's would happily whip up a batch of their Secret Sauce. Seeing as there is so much pressure on engine builders to squeeze more HP, more fuel mileage, and better durability, I'm thinking that a special motor oil could certainly help.
What viscosities? Likely a 0W-5 or 0W-10 for qualifying and more like a 20W-40 or 20W-50 for the race, depending on track, race length, weather, etc. Could be anything, though. Those viscosities are plausible guesses.